Question: Multiply the following complex numbers: $({-3+4i}) \cdot ({-2-5i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3+4i}) \cdot ({-2-5i}) = $ $ ({-3} \cdot {-2}) + ({-3} \cdot {-5}i) + ({4}i \cdot {-2}) + ({4}i \cdot {-5}i) $ Then simplify the terms: $ (6) + (15i) + (-8i) + (-20 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 6 + (15 - 8)i - 20i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 6 + (15 - 8)i - (-20) $ The result is simplified: $ (6 + 20) + (7i) = 26+7i $